Loading monotonicity of weighted premiums, and total positivity properties of weight functions
Name
1806.07957.pdf
Description
Accepted version
Size
273.74 KB
Format
Adobe PDF
Checksum (MD5)
7478212886d7c545d8dafae5baba4589
Author(s)
Richards, Donald
Uhler, Caroline
Date Issued
2019
Journal
Journal of Mathematical Analysis and Applications
Publisher
Elsevier BV
Version
Author's final manuscript
Abstract
© 2019 Elsevier Inc. We consider the construction of insurance premiums that are monotonically increasing with respect to a loading parameter. By introducing weight functions that are totally positive of higher order, we derive higher monotonicity properties of generalized weighted premiums; in particular, we deduce for weight functions that are totally positive of order three a monotonicity property of the variance-to-mean ratio, or index of dispersion, of the loss variable. We derive the higher order total positivity properties of some ratios that arise in actuarial and insurance analysis of combined risks. Further, we examine seven classes of weight functions that have appeared in the literature and we ascertain the higher order total positivity properties of those functions.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/j.jmaa.2019.02.054
